Dirac equation in the magnetic-solenoid field

Abstract

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.

23 pages, 2 figures, LaTex file

Cited by in corpus (7)

• Zero modes in a system of Aharonov-Bohm fluxes
• Density of states of relativistic and nonrelativistic two-dimensional electron gases in a uniform magnetic and Aharonov-Bohm fields
• Aharonov-Bohm effect in relativistic and nonrelativistic 2D electron gas: a comparative study
• Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene
• Coherent states of non-relativistic electron in magnetic-solenoid field
• Induced fractional valley number in graphene with topological defects
• Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime